2 Determine the equations that describe 100 KN the variation

2. Determine the equations that describe 100 KN the variations in N, V, and M as functions of the distance from the left end of the beam. (Note: You will need to determine four sets of functions, one set for each segment of the beam.) Plot the results of the functions for distances ranging from x = 0 meters to x = 15 m (i.e., draw the N, V, and M diagrams using the functions). 120 kN 15 kN/m 4 A 4 15 n

Solution

Axial load on beam is applied at point B. the axial load on beam = 100*3/5=60 kN

Vertical load at B=100*4/5=80 kN

vectical load at C=120 kN

uniform load at DE=15 kN/m

pins support at A and roller at E

reaction at A in horizontal direction = 60 kN(towards left)

vertical reaction at A can be determined using moment equilibrium at support E

15*A_v = (80*12)+(120*8)+(15*5*2.5)

A_v=140.5 kN

Vertical reaction at support B = 80+120+(15*5)-140.5=134.5 kN

x=0 to x=3 segment:

Axial load in segment = 60 kN(tension)

Shear force in segment=140.5 kN

Bending moment = 140.5*x=140.5x kNm

x=3 to x=7 segment:

Axial load in segment = 0 kN

Shear force in segment=140.5-80=60.5 kN

Bending moment = 140.5*x-80*(x-3)=60.5x+240 kNm

x=7 to x=10 segment:

Axial load in segment = 0 kN

Shear force in segment=140.5-80-120=-59.5 kN

Bending moment = 140.5x-80*(x-3)-120*(x-7)=-59.5x+1080 kNm

x=10 to x=15 segment:

Axial load in segment = 0 kN

Shear force in segment=140.5-80-120-15*(x-10)=90.5-15x kN

Bending moment in segment=140.5*x - 80*(x-3)-120*(x-7)-15(x-10)²/2=-59.5x+1080-7.5(x-10)²kNm